THE TRANSPORTATION OF GASES 181 requiring a much smaller number of impellers; the interstage passages, however, become rather complicated. The successive impellers in a multi-stage compressor, handling smaller and smaller volumes of air, should be designed on the principle of similar compressors if all stages are to be equally efficient. Since the revolutions per minute is the same for all impellers, the diameters and all the other dimensions should vary inversely as the cube root of the density. In practice, however, the impellers are divided into two or more groups, and each group designed for its own average conditions. Cooling. — The cooling of the gas during its passage through a multi-stage compressor is of paramount importance for high efficiency and low power consumption, and ample passages for cooling water must be provided in the dia phragms between the stages. For pressures below 50 Ib. per square inch, it i generally aimed to keep the temperature down to that corresponding to adiabati compression; while for higher pressures, isothermal compression is more usually aimed at by the introduction of inter coolers between groups of stages. In the latter case, the hydraulic efficiency is given on the basis of isothermal compression. For adiabatic compression, if the cooling is just enough to remove the heat above that corresponding to adiabatic compression: 'where S is the number of stages, while the other symbols have the same meaning as on page 176. If the cooling is such that each stage starts with the same temperature, the temperature corresponding to pi, then p2/pi = [1 + ehd, (7 - l) For strictly isothermal compression, In all these formulas axial inlet flow and radial impeller exit are assumed; for all other cases ua*/g should be replaced by the proper value for H. Theoretical Power. — The theoretical horsepower required to compress adia-batically and deliver 100 cu. ft. of gas per minute (initial pressure, p\ Ib. per square inch), is hp.a = 1.501pi[(p2/pi)°-29 — 1]; and for isothermal compression it is : hp.i = 1.004pi Iogio(p2/pi). Table 15 gives the ratio of the theoretical work for isothermal compression to that for adiabatic compression for the largest range of pressures likely to be met with in practice. TABLE 15 pz/pi ................................ 1.5 2.02.5 3456789 10 (Isoth. 4- Adiab.) ..................... 940 . 904. 875 . 85 . 812 .784 .763 . 744 . 728 . 715 . 703 Leakage. — To reduce the leakage between stages and from the inlet of the last stage to the atmosphere, labyrinth packings are usually provided. In general, the leakage may be assumed as about 3 per cent of the rated quantity, about two-thirds of this taking place between the inlet of the last stage and the atmosphere. This loss is fairly independent of the number of stages. Centrifugal Compressor Tests. — In making acceptance tests, the compressor is tested with no piping at the inlet, the air being taken directly into the unrestricted compressor inlet, which is to be at a distance from the wall or from the floor equal to at least its own diameter. At the discharge end a length of pipe. equal to about ten times the discharge diameter is attached. At about the middle